Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 1-2 - Cumulative Review - Page 152: 33



Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the Distributive Property to simplify the given expression, $ t-\{t-[3t-(2t-t)-t]-4t\}-t .$ $\bf{\text{Solution Details:}}$ Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the expression above is equivalent to \begin{array}{l}\require{cancel} t-\{t-[3t-(2t-t)-t]-4t\}-t \\\\= t-\{t-[3t-1(2t)-1(-t)-t]-4t\}-t \\\\= t-\{t-[3t-2t+t-t]-4t\}-t \\\\= t-\{t-1[3t]-1[-2t]-1[t]-1[-t]-4t\}-t \\\\= t-\{t-3t+2t-t+t-4t\}-t \\\\= t-1\{t\}-1\{-3t\}-1\{2t\}-1\{-t\}-1\{t\}-1\{-4t\}-t \\\\= t-t+3t-2t+t-t+4t-t \\\\= 4t .\end{array}
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